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using properties of determinant, prove t...

using properties of determinant, prove that `abs{:(y+k , y , y ),(y , y + k , y ),(y, y , y+k):}= k^(2) ( 3y + k)`

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Using the properties of determinats, show that |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^(2)(3y+k)

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+z...

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  2. Prove that: |[x+4,2x,2x],[2x,x+4,2x],[2x,2x,x+4]|=(5x+4)(4-x)^2.

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  3. using properties of determinant, prove that abs{:(y+k , y , y ),(y , y...

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  4. Prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^(3)...

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  5. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

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  6. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

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  7. Prove that: {:|(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+b^2,2a),(2b,-2a,1-a^2-...

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  8. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  9. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  10. Which of the following is correct

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  11. Find area of the triangle with vertices at the point given in the fol...

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  12. Find area of the triangle with vertices at the point given in the fol...

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  13. Find area of the triangle with vertices at the point given in the fol...

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  14. Show that points : A (a,b+c),B(b,c+a),C(c,a+b) are collinear.

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  15. Find the value of k if the area of the triangle is 4 sq. units whose v...

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  16. Find the value of k’ if the area of the triangle is 4 sq. units and ve...

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  17. Find equation of line joining (1, 2) and (3, 6) using determinants.

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  18. Find equation of line joining (3, 1) and (9, 3) using determinants.

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  19. If area of triangle is 35 sq. units with vertices (2,-6), (5, 4) and (...

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  20. Write Minors and Cofactors of the elements of following determinant : ...

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